Combining astrometry with the light-time effect: The case of VW Cep, zeta Phe and HT Vir

TL;DR

This paper presents a method combining astrometry and light-time effect analysis to determine the orbits and distances of third bodies in eclipsing binary systems, demonstrated on three specific systems with consistent results.

Contribution

The study introduces a new algorithm that merges astrometric data with minima timing analysis to fully describe the orbits of third bodies in binary systems.

Findings

Derived new orbital parameters for third bodies in three systems.

Estimated distances consistent with Hipparcos measurements.

Demonstrated the algorithm's effectiveness and consistency.

Abstract

Three eclipsing binary systems with astrometric orbit have been studied. For a detailed analysis two circular-orbit binaries (VW Cep and HT Vir) and one binary with an eccentric orbit (zeta Phe) have been chosen. Merging together astrometry and the analysis of the times of minima, one is able to describe the orbit of such a system completely. The O-C diagrams and the astrometric orbits of the third bodies were analysed simultaneously for these three systems by the least-squares method. The introduced algorithm is useful and powerful, but also time consuming, due to many parameters which one is trying to derive. The new orbits for the third bodies in these systems were found with periods 30, 221, and 261 yr, and eccentricities 0.63, 0.37, and 0.64 for VW Cep, zeta Phe, and HT Vir, respectively. Also an independent approach to compute the distances to these systems was used. The use of this algorithm to VW Cep gave the distance d=(27.90 +/- 0.29) pc, which is in excellent agreement with the previous Hipparcos result.